6.6.1.1.

Background and Data

One of the assumptions in using classical Shewhart SPC charts is that
the only source of variation is from part to part (or within subgroup
variation). This is the case for most continuous processing situations.
However, many of today's processing situations have different sources
of variation. The semiconductor industry is one of the areas where the
processing creates multiple sources of variation.

In semiconductor processing, the basic experimental unit is a silicon
wafer. Operations are performed on the wafer, but individual wafers can
be grouped multiple ways. In the diffusion area, up to 150 wafers are processed
in one time in a diffusion tube. In the etch area, single wafers are processed
individually. In the lithography area, the light exposure is done on sub-areas
of the wafer. There are many times during the production of a computer
chip where the experimental unit varies and thus there are different sources
of variation in this batch processing environment.

The following is a case study of a lithography process. Five sites are
measured on each wafer, three wafers are measured in a cassette (typically
a grouping of 24 - 25 wafers) and thirty cassettes of wafers are used in
the study. The width of a line is the measurement under study. There are
two line width variables. The first is the original data and the second
has been cleaned up somewhat. This case study uses the raw data. The entire
data table is 450 rows long with six columns.